Abstracts of papers appearing in "Topics in Recreational Mathematics Volume 3," edited by Charles Ashbacher. ISBN 978-1511641005

Abstracts of papers appearing in Topics in Recreational Mathematics Volume 3, edited by Charles Ashbacher. ISBN 978-1511641005

The Real Curse of the Bambino

Christopher J. Brown, Lyon Carter III, Paul M. Sommers

Middlebury College

psommers@middlebury.edu

Abstract

 If Babe Ruth had not spent his first five-plus years as a pitcher with the Boston Red Sox, would he still be wearing the home-run crown?  The authors show that if Ruth had been employed as an everyday player early in his career, the probability is greater than 50 percent that he would have hit 900 career home runs.  While skeptics might argue that no hitter – not even Babe Ruth – could hit more than 40 home runs per season during the dead ball era (before 1919) to reach the 900 home run mark, the authors show that the Bambino could have exceeded Hank Aaron’s 755 career home runs (later eclipsed by Barry Bonds’ 762) with near certainty.

If Midy Doesn’t Work, What Then?

David L. Emory

emory@kalexres.kendal.org

Abstract

 The research reported here can be compared and contrasted with that of Midy, the French mathematician of the early 1800’s.  Both involve the calculation of period lengths and adding the first and second halves of the resulting repetends. Midy worked with primes, but here the numbers are composites.  One set of factors is 7 and 13, and the other set is 73, 17, and 97. The interesting results here are quite different from Midy’s string of 9’s.

Magic Squares

Clarence A. Gipbsin

Smarandache’s Orthic Theorem

Edited by Prof. Ion Patrascu

Fratii Buzesti College

Craiova, Romania

Abstract

We present the Smarandache’s Orthic Theorem in the geometry of the triangle.

Exploring a Fascinating Integer Sequence

Jay L. Schiffman
Rowan University
schiffman@rowan.edu

Abstract

A number of years ago, a colleague asked his students to find all the prime outputs in the following integer sequence: 9, 98, 987, 9876, 98765, 987654, 9876543, 98765432, 987654321, 9876543219, 98765432198, 987654321987, etc. This article not only resolves this question, but pursues the sequence much further. Using MATHEMATICA and modular arithmetic, we will explore the prime factorizations and divisibility patterns in the sequence as well as suggest companion sequences and directions for additional stimulating research.

An Analysis of Multistate Lights Out on a Cube

John Antonelli
Crista Arangala
Elon University
ccoles@elon.edu

Abstract

 This paper analyzes the multistate Lights Out game on a cube. With the goal of the original lights out game being to get all of the lights off, we explore how to get all buttons from one state to the next on a cube with simultaneous presses.  Solutions for an arbitrary number of states is discussed and a gathering technique for general initial conditions is presented.

A Graphical Solution to the Montmort Matching Problem

Diego Castano
Nova Southeastern University

castanod@nova.edu

Abstract

 A graphical, or diagrammatic, method not relying on any formal combinatorial tools is used to solve a variation of the card matching problem. In the card problem, one is interested in determining the probability of matching cards from two shuffled decks on simultaneous draws. 

Behforooz Calendarical Magic Squares

Hossein Behforooz
Utica College

hbehforooz@utica.edu
www.utica.edu/hbehforooz

Abstract
 This is another interesting, fun topic in recreational mathematic.  Simply, select any month in any desktop or wall calendar and draw any three by three or four by four table and rearrange the date numbers in these tables to create different magic squares.  Yes MATH is fun and MATH is cool.